Model of random field with piece-constant values and sampling-restoration algorithm of its realizations

We propose a description of the model of a random piecewise constant field formed by the sum of realizations of two Markov processes with an arbitrary number of states and defined along mutually perpendicular axes. The number of field quantization levels can be arbitrary. Realizations of a random field model of the desired shape are created by appropriate selection of parameters for formative realization of Markov processes. For the proposed field model, we investigated the sampling and restoration algorithm of any selected realizations. As a result, we determined the optimal sampling and recovery algorithms. The resulting sampling is fundamentally non-periodic. Recovery errors are calculated. Two examples are considered.